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Forward-secure group signatures from lattices. (English) Zbl 07173856
Ding, Jintai (ed.) et al., Post-quantum cryptography. 10th international conference, PQCrypto 2019, Chongqing, China, May 8–10, 2019. Revised selected papers. Cham: Springer (ISBN 978-3-030-25509-1/pbk; 978-3-030-25510-7/ebook). Lecture Notes in Computer Science 11505, 44-64 (2019).
Summary: Group signature is a fundamental cryptographic primitive, aiming to protect anonymity and ensure accountability of users. It allows group members to anonymously sign messages on behalf of the whole group, while incorporating a tracing mechanism to identify the signer of any suspected signature. Most of the existing group signature schemes, however, do not guarantee security once secret keys are exposed. To reduce potential damages caused by key exposure attacks, Song (ACMCCS 2001) put forward the concept of forward-secure group signature (FSGS), which prevents attackers from forging group signatures pertaining to past time periods even if a secret group signing key is revealed at the current time period. For the time being, however, all known secure FSGS schemes are based on number-theoretic assumptions, and are vulnerable against quantum computers.
In this work, we construct the first lattice-based FSGS scheme. Our scheme is proven secure under the Short Integer Solution and Learning with Errors assumptions. At the heart of our construction is a scalable lattice-based key evolving mechanism, allowing users to periodically update their secret keys and to efficiently prove in zero-knowledge that key evolution process is done correctly. To realize this essential building block, we first employ the Bonsai tree structure by Cash et al. (EUROCRYPT 2010) to handle the key evolution process, and then develop Langlois et al.’s construction (PKC 2014) to design its supporting zero-knowledge protocol.
For the entire collection see [Zbl 1418.94003].

94A60 Cryptography
81P94 Quantum cryptography (quantum-theoretic aspects)
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